If Hall plates are used as magnetic field sensors they are usually powered up by a current source connected to a pair of non-neighboring contacts. The output voltage is tapped at another pair of non-neighboring contac...If Hall plates are used as magnetic field sensors they are usually powered up by a current source connected to a pair of non-neighboring contacts. The output voltage is tapped at another pair of non-neighboring contacts. In this paper we study more general operating conditions of Hall plates with an arbitrary number of contacts. In such hybrid operating modes current sources are connected to a first set of contacts and voltage sources to a second set of contacts. Output voltages are tapped at the first set of contacts and output currents are measured at the second set of contacts. All these output signals are multiplied by coefficients and added up. The purpose of this work is to figure out which operating mode and which Hall plate achieve maximum signal at minimum thermal noise and power dissipation. To this end we develop a theory, which gives the ratio of signal over noise and power as a function of the resistance matrix of Hall plates, of the supply voltages and currents, and of the coefficients. Optimization is done analytically in closed form and numerically for specific examples. The results are: 1) all operating modes have identical noise performance if their parameters are optimized;2) for any Hall plate one can measure its resistance matrix and insert its values into our formulae to obtain the optimum supply currents and coefficients for optimum noise performance.展开更多
本文对P.Heywood研究的广义积分:integral from 0 to 1 (f(x)/(1-x)~W dx)进行了探讨。在莫叶、陈留琨、霍守诚、蒋润勃等人的研究基础上,将结果推广到:W=4,或4<W<5。 主要内容如下: 定理:设a_#终归为正,且: sum from n=0 to ∞ (...本文对P.Heywood研究的广义积分:integral from 0 to 1 (f(x)/(1-x)~W dx)进行了探讨。在莫叶、陈留琨、霍守诚、蒋润勃等人的研究基础上,将结果推广到:W=4,或4<W<5。 主要内容如下: 定理:设a_#终归为正,且: sum from n=0 to ∞ (a_n)=sum from n=0 to ∞ ((n+1)a_n) =sum from n=0 to ∞ (n(n-1)(n+1)(n+2)an) =sum from n=0 to ∞ (n(n-1)(n-2)(n+1)(n+2)(n+3)an) =0 f(x)=sum from n=0 to ∞ (a_np_n(x)) 这里:P_π(x)为Legendre多项式,则按照: w=4,或4<w<5,积分: I(?)=intergal form 0 to 1(f(x)/(1-x)~w dx) 存在的充要条件是: 级数∑n^(?)a_nlogn,或级数∑n^2(w^(-1))a_n收敛。展开更多
文摘If Hall plates are used as magnetic field sensors they are usually powered up by a current source connected to a pair of non-neighboring contacts. The output voltage is tapped at another pair of non-neighboring contacts. In this paper we study more general operating conditions of Hall plates with an arbitrary number of contacts. In such hybrid operating modes current sources are connected to a first set of contacts and voltage sources to a second set of contacts. Output voltages are tapped at the first set of contacts and output currents are measured at the second set of contacts. All these output signals are multiplied by coefficients and added up. The purpose of this work is to figure out which operating mode and which Hall plate achieve maximum signal at minimum thermal noise and power dissipation. To this end we develop a theory, which gives the ratio of signal over noise and power as a function of the resistance matrix of Hall plates, of the supply voltages and currents, and of the coefficients. Optimization is done analytically in closed form and numerically for specific examples. The results are: 1) all operating modes have identical noise performance if their parameters are optimized;2) for any Hall plate one can measure its resistance matrix and insert its values into our formulae to obtain the optimum supply currents and coefficients for optimum noise performance.
文摘本文对P.Heywood研究的广义积分:integral from 0 to 1 (f(x)/(1-x)~W dx)进行了探讨。在莫叶、陈留琨、霍守诚、蒋润勃等人的研究基础上,将结果推广到:W=4,或4<W<5。 主要内容如下: 定理:设a_#终归为正,且: sum from n=0 to ∞ (a_n)=sum from n=0 to ∞ ((n+1)a_n) =sum from n=0 to ∞ (n(n-1)(n+1)(n+2)an) =sum from n=0 to ∞ (n(n-1)(n-2)(n+1)(n+2)(n+3)an) =0 f(x)=sum from n=0 to ∞ (a_np_n(x)) 这里:P_π(x)为Legendre多项式,则按照: w=4,或4<w<5,积分: I(?)=intergal form 0 to 1(f(x)/(1-x)~w dx) 存在的充要条件是: 级数∑n^(?)a_nlogn,或级数∑n^2(w^(-1))a_n收敛。
